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Absolute value is a mathematician's way of judging numbers by their magnitude rather than their positive/negative value. It is the distance of the number from 0 on a number line.

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How many ordered pairs \((x, y)\) are there such that \(x\) is a nonzero integer that satisfies \(-8\leq x \leq 8\), \(y\) is a nonzero integer that satisfies \(-2\leq y \leq 2\), and \[\lvert x+y \rvert = \lvert x \rvert + \lvert y \rvert?\]

**Details and assumptions**

For an **ordered pair of integers** \((a,b)\), the order of the integers matter. The ordered pair \((1, 2)\) is different from the ordered pair \((2,1) \).

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How many ordered triples of integers \( (a, b, c) \) subject to \( -20 < a < b < c < 20,\) are there, such that

\[ \left| a + b + c \right | = |a| + |b| + |c|? \]

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